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Mathematics
Problem
Assertion: If system of equations
2
x
+
3
y
=
a
2x + 3y = a
2
x
+
3
y
=
a
and
b
x
+
4
y
=
5
bx + 4y = 5
b
x
+
4
y
=
5
has infinite solution, then
a
=
15
4
,
b
=
8
5
a = \frac{15}{4}, b = \frac{8}{5}
a
=
4
15
,
b
=
5
8
Reason: Straight lines
a
1
x
+
b
1
y
+
c
1
=
0
a_1 x + b_1 y + c_1 = 0
a
1
x
+
b
1
y
+
c
1
=
0
and
a
2
x
+
b
2
y
+
c
2
=
0
a_2 x + b_2 y + c_2 = 0
a
2
x
+
b
2
y
+
c
2
=
0
are parallel, if
a
1
a
2
=
b
1
b
2
≠
c
1
c
2
\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}
a
2
a
1
=
b
2
b
1
=
c
2
c
1
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